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by Rishi Sat Jun 01, 2013 9:49 am
When you studied Calculus at IIT, did the teacher explain why we need to use Taylor's series?
https://class.coursera.org/calcsing-002/lecture/278
https://class.coursera.org/calcsing-002/lecture/278
Rishi- Posts : 5129
Join date : 2011-09-02
Re: To MAx
by MaxEntropy_Man Sat Jun 01, 2013 10:03 am
such a long time ago, i don't remember when i learned the utility of a taylor series. i haven't watched your video, but taylor expansions are the correct and rigorous way to look at the behavior of a continuous function around a fixed point. when you do linear interpolation you are basically ignoring terms O(x^2) and higher in comparison with the linear terms. there are many instances in natural science where higher order terms become critically important. for example when you are studying the thermodynamics of certain types of phase transformations in materials, one needs to examine a certain thermodynamic function called the gibbs free energy and exapand it as a function of some thermodynamic property, say the composition of the material. in this endeavor, higher order terms become crucial. without the higher order terms, thermodynamics will incorrectly predict that you don't have any phase transformations.
MaxEntropy_Man- Posts : 14702
Join date : 2011-04-28
Re: To MAx
by Seva Lamberdar Sat Jun 01, 2013 10:35 am
https://class.coursera.org/calcsing-002/lecture/278[/quote[/url]]Rishi wrote:When you studied Calculus at IIT, did the teacher explain why we need to use Taylor's series?
[url=https://class.coursera.org/calcsing-002/lecture/278
There are many ways to represent a function ... Taylor's series is one of them, quite simple and easy to use.
Seva Lamberdar- Posts : 6594
Join date : 2012-11-29 -
Re: To MAx
by Rishi Sat Jun 01, 2013 5:46 pm
https://class.coursera.org/calcsing-002/lecture/12
IN the above video, the teacher shows that by using expansion of series, the in-line electrostatic potential of dipole is stronger than the orthogonal electrostatic potential of a dipole. He ignores the Higher Order Terms.
IN the above video, the teacher shows that by using expansion of series, the in-line electrostatic potential of dipole is stronger than the orthogonal electrostatic potential of a dipole. He ignores the Higher Order Terms.
Rishi- Posts : 5129
Join date : 2011-09-02
Re: To MAx
by MaxEntropy_Man Sat Jun 01, 2013 6:13 pm
Rishi wrote:https://class.coursera.org/calcsing-002/lecture/12
IN the above video, the teacher shows that by using expansion of series, the in-line electrostatic potential of dipole is stronger than the orthogonal electrostatic potential of a dipole. He ignores the Higher Order Terms.
yes in his problem the higher order terms were not required. the way he analyzed the dipole is a simple example of a broader analytical technique called asymptotic analysis which you employ to find out how many leading terms you need to retain to reproduce the observed physical behavior. the ultimate proof of the correctness of the analysis of course has to come from experiment.
in the case i wrote about in my earlier post, discarding the higher order terms leads to incorrect physics and does not reproduce the observed behavior.
MaxEntropy_Man- Posts : 14702
Join date : 2011-04-28
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